Optoelectronic equalizer circuit

ABSTRACT

We disclose an optoelectronic circuit that is configurable to operate as an FIR filter, in which the tapping and the weighting of the signal that is being equalized are performed in the optical domain, whereas the summation of the weighted signals is performed in the electrical domain after the corresponding optical signals are converted into electrical form using an array of photodetectors. Photodetectors in the array are arranged such that some of them contribute to the equalized electrical signal with a positive polarity and the others contribute to the equalized electrical signal with a negative polarity. As a result, at least some of the tap weights used in the FIR filter can be made variable between a positive value and a negative value.

BACKGROUND

1. Field

The present disclosure relates to optical communication equipment and,more specifically but not exclusively, to optoelectronic circuits.

2. Description of the Related Art

This section introduces aspects that may help facilitate a betterunderstanding of the disclosure. Accordingly, the statements of thissection are to be read in this light and are not to be understood asadmissions about what is in the prior art or what is not in the priorart.

The next-generation of optical communication systems is being designedfor relatively high data rates, e.g., higher than about 100 Gbit/s perchannel. At these rates, the effects of bandwidth limitations of variouscomponents of the transmitter, fiber-optic channel, and/or receiver maysignificantly degrade the performance of optical transport links. Oneapproach to dealing with these effects is to perform appropriate signalprocessing, e.g., signal equalization in the electrical digital domain,after the corresponding optical signal has been photo-detected anddigitized at the receiver. This electrical digital-signal processing istypically implemented using a customized ASIC or DSP, which can berelatively expensive to design and/or make.

SUMMARY OF SOME SPECIFIC EMBODIMENTS

Disclosed herein are various embodiments of an optoelectronic circuitconfigurable to operate as a finite-impulse-response (FIR) filter, inwhich the tapping and the weighting of the signal that is beingequalized are performed in the optical domain, whereas the summation ofthe weighted signals is performed in the electrical domain after thecorresponding optical signals are converted into electrical form usingan array of photodetectors. Photodetectors in the array are arrangedsuch that some of the photodetectors contribute to the equalizedelectrical signal with a positive polarity and the others contribute tothe equalized electrical signal with a negative polarity. As a result,at least some of the tap weights used in the FIR filter can be madevariable between a positive value and a negative value.

In some embodiments, the disclosed optoelectronic circuit mayadvantageously be used to reduce the signal-processing load of and/orthe signal-processing requirements to the receiver's electrical DSP.

According to one embodiment, provided is an apparatus comprising: anarray of photodetectors; an optical splitter having an optical inputport and a plurality of optical output ports, with each of the opticaloutput ports being connected to illuminate a respective one of thephotodetectors in the array of photodetectors; a bank of optical delayelements, with each of the optical delay elements being coupled betweena respective one of the optical output ports and the respective one ofthe photodetectors such that light of each of the optical output portspasses through a respective one of the optical delay elements; and anarray of variable optical-gain elements coupled between the opticalsplitter and the array of photodetectors such that, for at least some ofthe optical output ports, the light also passes through a respective oneof the variable optical-gain elements. Each photodetector in the arrayof photodetectors is configured to convert received light into arespective electrical signal. The apparatus further comprises anelectrical signal combiner configured to combine the respectiveelectrical signals to generate an electrical output signal in a mannerthat causes a first subset of the photodetectors and a second subset ofthe photodetectors to contribute the respective electrical signals tothe electrical output signal with opposite polarities.

According to another embodiment, provided is an apparatus comprising: anoptical splitter having an optical input port and a plurality of opticaloutput ports; an array of variable optical-gain elements, each coupledto receive light from a respective one of the optical output ports andconfigured to generate a respective attenuated or amplified light beam;a bank of optical delay elements, each connected to a respective one ofthe variable optical-gain elements and configured to delay therespective attenuated or amplified light beam by a respective delay timeto produce a respective delayed light beam, wherein a set of therespective delay times has at least three different values; an array ofphotodetectors, each coupled to receive light from a respective one ofthe optical delay elements and configured to convert the respectivedelayed light beam into a respective electrical signal; and anelectrical signal combiner configured to combine the respectiveelectrical signals to generate an electrical output signal in a mannerthat causes a first subset of the photodetectors and a second subset ofthe photodetectors to contribute the respective electrical signals tothe electrical output signal with opposite polarities.

According to yet another embodiment, provided is an apparatuscomprising: an optical splitter having an optical input port and firstand second optical output ports; a first variable optical-gain elementcoupled to receive light from the first optical output port andconfigured to generate a first attenuated or amplified light beam; asecond variable optical-gain element coupled to receive light from thesecond optical output port and configured to generate a secondattenuated or amplified light beam; a first optical delay elementconfigured to delay the first attenuated or amplified light beam by afirst delay time to produce a first delayed light beam; a second opticaldelay element configured to delay the second attenuated or amplifiedlight beam by the first delay time to produce a second delayed lightbeam; a first photodetector configured to convert the first delayedlight beam into a first electrical signal; a second photodetectorconfigured to convert the second delayed light beam into a secondelectrical signal; and an electrical circuit configured to generate anelectrical output signal using the first and second electrical signals,wherein the first and second electrical signals are combined withopposite polarities. The first and second variable optical-gain elementsare tunable such that a combined contribution of the first and secondelectrical signals into the electrical output signal is variable betweenbeing positive and being negative.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and benefits of various disclosed embodimentswill become more fully apparent, by way of example, from the followingdetailed description and the accompanying drawings, in which:

FIG. 1 shows a block diagram of an optoelectronic circuit according toan embodiment of the disclosure;

FIG. 2 shows a circuit diagram of an optoelectronic circuit that can beused in the optoelectronic circuit of FIG. 1 according to an embodimentof the disclosure;

FIG. 3 shows a top view of an integrated optoelectronic circuitaccording to another embodiment of the disclosure; and

FIG. 4 shows a top view of an integrated optoelectronic circuitaccording to yet another embodiment of the disclosure.

DETAILED DESCRIPTION

In an example embodiment, an optoelectronic circuit disclosed herein maybe a part of the host optical receiver that enables the latter toperform at least some of the desired signal processing outside thereceiver's electrical DSP. The signal processing implemented in theoptoelectronic circuit can be used, e.g., to at least partiallycompensate the adverse effects of chromatic dispersion,polarization-mode dispersion, inter-symbol interference, and/or narrowpassband filtering imposed on the received communication signal(s) bythe various components of the transmitter, fiber-optic channel, and/orreceiver. This capability may advantageously reduce thesignal-processing load of and/or the signal-processing requirements tothe receiver's electrical DSP.

FIG. 1 shows a block diagram of an optoelectronic circuit 100 accordingto an embodiment of the disclosure. Circuit 100 is configured to receivean optical input signal 102 and convert this optical input signal intoan electrical output signal 152, e.g., as further described below.Optical input signal 102 may be modulated with data using any suitablemodulation format, such as NRZ (non-return-to-zero), PAM(pulse-amplitude modulation), QPSK (quadrature phase-shift keying), QAM(quadrature amplitude modulation), etc. Electrical output signal 152 maybe an electrical analog signal that may be subjected to furtherconversion into an electrical digital form in an analog-to-digitalconverter (not explicitly shown in FIG. 1), e.g., for further processingin an electrical DSP (not explicitly shown in FIG. 1). In someembodiments, an electronic controller 160 may be used, e.g., as furtherexplained below, to configure circuit 100 to operate as a finite impulseresponse (FIR) filter. As known in the relevant art, one or more FIRfilters may be used to implement an adaptive signal equalizer for acommunication system.

Circuit 100 comprises a 1×N optical splitter 110 configured to splitoptical input signal 102 into N (attenuated) copies 112 ₁-112 _(N),where N is a positive integer greater than one. For illustrationpurposes and without any implied limitation, FIG. 1 shows an embodimentcorresponding to N>3. In an example embodiment, splitter 110 may be anoptical power splitter. In various embodiments, signal copies 112 ₁-112_(N) may have the same optical power (intensity) or different respectiveoptical powers.

Signal copies 112 ₁-112 _(N) produced by splitter 110 are applied to anarray 120 of variable optical attenuators A₁-A_(N) as indicated inFIG. 1. The attenuation applied by each of attenuators A₁-A_(N) can beindividually changed using a control signal 162 generated by controller160. The attenuated optical signals produced by attenuators A₁-A_(N) arelabeled 122 ₁-122 _(N).

Each of optical signals 122 ₁-122 _(N) is applied to a respective one ofdelay elements (or delay lines) D₁-D_(N) of an optical-delay bank 130.The delayed optical signals produced by delay elements D₁-D_(N) arelabeled 132 ₁-132 _(N), respectively. In some embodiments, each of delayelements D₁-D_(N) in optical-delay bank 130 may be a fixed delay elementconfigured to apply a respective fixed delay time τ_(n) to a respectiveone of optical signals 122 ₁-122 _(N), where n=1, 2, . . . , N. In someother embodiments, some or all of delay elements D₁-D_(N) inoptical-delay bank 130 may be individually tunable to apply a respectivevariable delay time τ_(n) to the respective one of optical signals 122₁-122 _(N). In this case, the values of τ_(n) may be appropriatelyselected from the range of variability of the delay elements and thenspecified to the delay elements in optical-delay bank 130 by controller160 via a control signal 164. Example tunable delay lines that can beused to implement variable delay elements D₁-D_(N) are disclosed, e.g.,in commonly owned U.S. Pat. No. 6,956,991, which is incorporated hereinby reference in its entirety.

In various embodiments, the set T={τ₁, τ₂, . . . , τ_(N)} of delay timesused in optical-delay bank 130 may contain any desired number ofdistinct delay values. For example, in one embodiment, the set T maycontain N distinct delay values. In an alternative embodiment, the set Tmay contain N/2 distinct delay values such that, for any delay timeτ_(j), there is exactly one other delay time τ_(k) (where k≠j) of thesame nominal value, i.e., τ_(k)=τ_(j). A person of ordinary skill in theart will understand that, depending on the intended signal-processingfunction of circuit 100, other numbers of distinct delay values in theset T may also be used.

In some embodiments, some (e.g., at least one) of delay elementsD₁-D_(N) may be configured to introduce a delay time of a nominally zerovalue. As used herein the term “nominally zero” should be construed tomean that the corresponding delay time is much smaller (e.g., by afactor of ≧10) than the smallest of the other delay times in the set T.In general, any optical element (even a short straight piece of opticalwaveguide in an optical waveguide circuit) acts as a “delay element”because a light wave travels at a finite rate of speed and, as such, canonly traverse an optical element in a finite amount of time, which isthe “delay time” of that optical element.

Delayed optical signals 132 ₁-132 _(N) produced by delay elementsD₁-D_(N) of optical-delay bank 130 are applied to an array 140 ofphotodetectors (e.g., photodiodes) PD₁-PD_(N) where these opticalsignals are converted into the corresponding electrical signals (e.g.,electrical currents) labeled 142 ₁-142 _(N). An electrical signalcombiner 150 then operates to combine electrical signals 142 ₁-142 _(N),e.g., as further described below, to generate electrical output signal152. Depending on the technology used to manufacture circuit 100, thecircuit may have up to one hundred or even up to one thousandphotodetectors in array 140 (e.g., N≦1000).

An important feature of electrical signal combiner 150 is that it isconfigured to combine electrical signals 142 ₁-142 _(N) such that someof these signals contribute to electrical output signal 152 with apositive polarity, and the remainder of these signals contributes toelectrical output signal 152 with a negative polarity. This property ofelectrical signal combiner 150 can be mathematically expressed, forexample, as follows:

$\begin{matrix}{V_{152} = {Z_{0}\left( {{\sum\limits_{n \in S^{+}}i_{n}} - {\sum\limits_{n \in S^{-}}i_{n}}} \right)}} & (1)\end{matrix}$

where V₁₅₂ is the voltage of signal 152; Z₀ is the output impedance ofelectrical signal combiner 150; i_(n) is the photocurrent generated byphotodetector PD_(n) (where n=1, 2, . . . , N); S⁺ denotes the subset ofthe values of n corresponding to the photodetectors of array 140 thatcontribute to signal 152 with the positive polarity; and S⁻ denotes thesubset of the values of n corresponding to the photodetectors of array140 that contribute to signal 152 with the negative polarity. In variousembodiments, subsets ,S⁻ and S⁻ may have the same number of elements ordifferent respective numbers of elements.

In some embodiments, each or some of variable optical attenuatorsA₁-A_(N) in array 120 may be replaced by the corresponding variable-gainoptical amplifier(s), i.e., elements A₁-A_(N) in array 120 can bemore-generally characterized as variable optical-gain elements. A personof ordinary skill in the art will understand that, similar to variableoptical attenuators, variable-gain optical amplifiers can provide meansfor controllably changing the values of filter-tap coefficients, e.g.,using controller 160 and control signal 162, when circuit 100 isconfigured to operate as an FIR filter.

Hereafter, the term “variable optical-gain element” is used as a generalterm that covers both a variable optical attenuator and a variable-gainoptical amplifier. For example, in one embodiment, a variableoptical-gain element can be a variable optical attenuator. In this case,the variable optical gain of such “variable optical-gain element” issmaller than one. In an alternative embodiment, a variable optical-gainelement can be a variable-gain optical amplifier. In this case, thevariable optical gain of such “variable optical-gain element” is greaterthan one. For illustration purposes, the subsequent description ofexample embodiments is given in reference to variable opticalattenuators. Based on the provided description, a person of ordinaryskill in the art will understand how to make and use embodiments thatemploy variable-gain optical amplifier instead of or in addition tovariable optical attenuators.

In some embodiments, array 120 may have fewer than N variableoptical-gain elements. For example, in one alternative embodiment, array120 may have N−1 variable optical-gain elements. In another alternativeembodiment, array 120 may have N−2 variable optical-gain elements.

In some embodiments, the positions of array 120 and bank 130 in circuit100 can be swapped. More specifically, in such embodiments, bank 130 isdirectly connected to splitter 110, and then array 120 is connectedbetween bank 130 and array 140.

FIG. 2 shows a circuit diagram of an optoelectronic circuit 200 that canbe used in optoelectronic circuit 100 (FIG. 1) according to anembodiment of the disclosure. More specifically, circuit 200 may be usedin place of photodetector array 140 and electrical signal combiner 150(see FIG. 1). For illustration purposes and without any impliedlimitation, FIG. 2 shows an embodiment corresponding to N>7. Based onthe provided description, a person of ordinary skill in the art willunderstand how to make and use other embodiments of circuit 200corresponding to other values of N.

The N photodiodes PD₁-PD_(N) in circuit 200 are all connected to acommon electrical line 252 and configured to receive optical signals 132₁-132 _(N), respectively (also see FIG. 1). Electrical line 252 isconfigured to collect the photocurrents generated by photodiodesPD₁-PD_(N), and the resulting combined photocurrent causes outputvoltage V₁₅₂ to be generated at the output terminal (labeled 152) ofcircuit 200. Photodiodes PD₁-PD_(N) are appropriately electricallybiased and are electrically connected to capacitors C₁-C_(N) asindicated in FIG. 2. The output impedance Z₀ (e.g., =50 Ohm) for circuit200 may be achieved, for example, by having two resistors, each havingthe resistance of 2Z₀, connected between common electrical line 252 andthe ground terminals as further indicated in FIG. 2.

Photodiodes PD₁, PD₃, PD₅, . . . , PD_(N−1) in circuit 200 have theircathodes directly electrically connected to common electrical line 252and, as such, draw the current from the common electrical line. Thus,each of photodiodes PD₁, PD₃, PD₅, . . . , PD_(N−1) is configured tocontribute to output voltage V₁₅₂ with a negative polarity. In contrast,photodiodes PD₂, PD₄, PD₆, . . . , PD_(N) have their anodes directlyelectrically connected to common electrical line 252 and, as such, applythe current to the common electrical line. Thus, each of photodiodesPD₂, PD₄, PD₆, . . . , PD_(N) is configured to contribute to outputvoltage V₁₅₂ with a positive polarity. The output voltage V₁₅₂ generatedby circuit 200 at output terminal 152 can be described by Eq. (1),wherein S⁺={2, 4, 6, . . . , N} and AS⁺={1, 3, 5, . . . , N−1}.

Capacitors C₁-C_(N) are configured to provide an RF ground for thephotodiodes. Since capacitors C₁, C₃, C₅, . . . , C_(N−1) are connectedin parallel, in some embodiments, this array of capacitors can berealized using a single capacitor having the combined capacitance ofthese capacitors. One of the design specifications may be that thecapacitive reactance of the array of smaller capacitors C₁, C₃, C₅, . .. , C_(N−1) or of the equivalent single larger capacitor is sufficientlysmall compared to the complex impedance of the photodiode array toprovide a good RF return path for circuit 200. A similar descriptionapplies also to capacitors C₂, C₄, C₆, . . . , C_(N). In someembodiments, e.g., embodiments designed for handling communicationsignals having relatively long data-sequence lengths (e.g., PRBS-15 orgreater), relatively large capacitors may be needed in place ofcapacitor banks (C₁, C₃, C₅, . . . , C_(N−1)) and (C₂, C₄, C₆, . . . ,C_(N)) to enable circuit 200 to properly process the relatively lowfrequency components associated with such data-sequence lengths. Inthese embodiments, to obtain a desired capacitance, additionallarger-size capacitors located off-chip may be connected in parallel tothe on-chip capacitors shown in FIG. 2.

The use of the two resistors of resistance 2Z₀, connected as indicatedin FIG. 2, provide only one possible realization of electrical impedancematching of the array of photodiodes PD₁-PD_(N) to the external systemimpedance. A person of ordinary skill in the art will understand thatother impedance-matching schemes can also be used for this purpose. Ingeneral, impedance matching may be realized using any suitablecombination of resistive and reactive components. Alternatively, inembodiments where the array of photodiodes PD₁-PD_(N) is directlyelectrically connected to a transimpedance amplifier (not explicitlyshown in FIG. 2), the impedance matching may not be needed at all, e.g.,because circuit 200 can operate as an input-current source for thetransimpedance amplifier.

Further features of optoelectronic circuits 100 and 200 are described inmore detail below in reference to several specific illustrativeembodiments. These embodiments may differ from one another, e.g., in thevalue of N and/or the number of distinct delay values in the set T={τ₁,τ₂, . . . , τ_(N)}.

In a first illustrative embodiment, optical splitter 110 may beconfigured to generate signal copies 112 ₁-112 _(N) of equal intensityp₀, and optical-delay bank 130 is configured such that the set T={τ₁,τ₂, . . . , τ_(N)} has N distinct delay values defined by Eq. (2):

τ_(n)=n τ₀   (2)

where τ₀ is a constant. In this embodiment, output signal 152 can beapproximately described by Eq. (3):

V ₁₅₂ =Z ₀ p ₀ η(−a ₁ exp(−jωτ ₀)+a ₂ exp(−j2ωτ₀)−a ₃ exp(−j3ωτ₀)+a ₄exp(−j4ωτ₀)− . . . . . . −a _(N−1) exp(−j(N−1)ωτ₀)+a _(N) exp(−jNωτ ₀))  (3)

where η is the nominal responsivity of each of photodiodes PD₁-PD_(N); ωis the angular frequency; and a_(n) is the signal-attenuation factor(0≦a_(n)<1) imposed by optical attenuator A_(n) in array 120. Aftersubstituting z=exp(jωτ₀) into Eq. (3) and renormalizing the resultingformula by factoring out some common factors, one finds that the rightside of Eq. (3) can be expressed using function H(z) given by Eq. (4):

H(z)=−a ₁ +a ₂ z ⁻¹ −a ₃ z ⁻² +a ₄ z ⁻³ − . . . −a _(N) z ^(−N+2) +a_(N) z ^(−N+1)   (4)

An alternative mathematical expression for the function H(z) can beobtained by normalizing the right part of Eq. (4) by dividing it by −a₁.This type of normalization results in the first term of the normalizedfunction H(z) to be one.

A person of ordinary skill in the art will recognize that Eq. (4) (orits normalized version) describes a z-transform of an FIR filter having(N−1) uniformly spaced taps, wherein the sign of the tap coefficientsalternates from one tap to the immediate next tap. It means that thefirst embodiment of circuit 100 can be used as an FIR filter whosetransfer function has this specific (i.e., sign-alternating) property ofits tap coefficients. The sign of each particular tap coefficient isfixed, being either negative or positive. However, the absolute value ofeach tap coefficient can be changed, as appropriate or necessary, e.g.,by individually tuning each of optical attenuators A₁-A_(N) in array 120(see FIG. 1).

Note that an FIR filter implemented using circuits 100 and 200 has itsdelay and signal-weighting elements operating in the optical domain (seeoptical elements 120 and 130, FIG. 1), whereas the weighted-signal adderoperates in the electrical domain (see electrical signal combiner 150,FIG. 1). In contrast, a conventional FIR filter has all of these threemain FIR-filter elements operating in the same domain, either optical orelectrical.

In a second illustrative embodiment, optical splitter 110 may beconfigured to generate signal copies 112 ₁-112 _(N) of equal intensityp₀, where N is even; and optical-delay bank 130 is configured such thatthe set T={τ₁, τ₂, . . . , τ_(N)} has N/2 distinct delay values definedby Eqs. (5a)-(5b):

τ_(2k−1)=(2k+1) τ₀   (5a)

τ_(2(k+1))=(2k+1) τ₀   (5b)

where k=0, 1, 2, . . . , 0.5N−1, and τ₀ is a constant. In thisembodiment, circuit 100 can operate as an FIR filter whose transferfunction is represented by the following z-transform:

H(z)=(−a ₁ +a ₂)+(−a ₃ +a ₄)z ⁻¹+(−a ₅ +a ₆)z ⁻²+ . . . +(−a _(N−1) +a_(N))z ^(−(0.5N−1))   (6)

This particular FIR filter has (0.5N−1) uniformly spaced taps. Both thesign and absolute value of each tap coefficient in this FIR filter canbe changed by appropriately tuning optical attenuators A₁-A_(N) in array120 (see FIG. 1). For example, the sign of the zero-order tapcoefficient (=−a₁+a₂) in this FIR filter can be changed by appropriatelytuning optical attenuators A₁ and A₂. More specifically, the zero-ordertap coefficient is positive when optical attenuators A₁ and A₂ are tunedsuch that a₁<a₂, and negative when optical attenuators A₁ and A₂ aretuned such that a₁>a₂. Similarly, the sign of the first-order tapcoefficient (=−a₃+a₄) in this FIR filter can be changed by appropriatelytuning optical attenuators A₃ and A₄. More specifically, the first tapcoefficient is positive when a₃<a₄, and negative when a₃>a₄. The sign ofthe second-order tap coefficient (=−a₅+a₆) in this FIR filter can bechanged by appropriately tuning optical attenuators A₅ and A₆, and soon.

FIG. 3 shows a top view of an integrated optoelectronic circuit 300according to another embodiment of the disclosure. Circuit 300 may beconsidered as an embodiment of circuit 100 (FIG. 1) corresponding toN=3. All components of circuit 300 may be fabricated on a common planarsubstrate 301 using a silicon photonic technology.

Circuit 300 has an input waveguide 302 configured to feed light into anoptical-waveguide structure comprising two optical-waveguideMach-Zehnder interferometers (MZI's) 304 ₁ and 304 ₂ interconnected asindicated in FIG. 3. The three output waveguides of thisoptical-waveguide structure are labeled 322 ₁-322 ₃, respectively. Onearm of MZI 304 ₁ has a thermoelectric phase shifter 306 ₁. One arm ofMZI 304 ₂ similarly has a thermoelectric phase shifter 306 ₂.

The relative intensity of light in waveguides 322 ₁-322 ₃ can be changedby appropriately tuning phase shifters 306 ₁ and 306 ₂, which can beaccomplished by changing their respective temperatures using controlsignals 362 ₁ and 362 ₂. In an example embodiment, a control signal 362may be an externally generated voltage applied to a respective pair ofelectrical-contact pads 308 and configured to resistively heat therespective phase shifter 306. The generated heat changes the temperatureof the phase shifter, which alters the index of refraction of theunderlying optical waveguide, thereby changing the optical phase shiftaccumulated in the waveguide by the propagating light. A change in theoptical phase shifts generated in phase shifters 306 ₁ and 306 ₂ cancause a change in the relative intensity of light in waveguides 322₁-322 ₃ because these optical phase shifts affect the interferencepatterns of the light beams that reach each of those waveguides throughthe different optical paths provided by the optical-waveguide structurebetween waveguide 302 and waveguides 322 ₁-322 ₃. Thus, theoptical-waveguide structure located between waveguide 302 and waveguides322 ₁-322 ₃ is configured to operate both as an optical splitteranalogous to optical splitter 110 (FIG. 1) and as a variable attenuatoranalogous to attenuator array 120 (FIG. 1).

Each of waveguides 322 ₁-322 ₃ is connected to a respective one ofwaveguides 332 ₁-332 ₃ via a respective one of fixed delay lines D₁-D₃.Each of delay lines D₁-D₃ comprises a different respective length ofoptical waveguide. The waveguides in delay lines D₂ and D₃ are arrangedin a double-spiral pattern to reduce the substrate-surface area taken upby those delay lines. Delay line D₁ has the shortest length among thethree delay lines and, as such, imposes the shortest delay time. Delayline D₃ has the longest length among the three delay lines and, as such,imposes the longest delay time. In an example embodiment, the delaytimes imposed by delay lines D₁-D₃ are τ₁, τ₁+τ₀, and τ₁+2τ₀,respectively. In some embodiments, τ₁=τ₀. In some embodiments, τ₀ to mayhave the value of 4 ps.

Waveguides 332 ₁-332 ₃ are configured to feed light into photodiodesPD₁-PD₃, respectively. A relatively large capacitor labeled C₁+C₃ thatis electrically connected between a first ground terminal 354 ₁ andphotodiodes PD₁ and PD₃ is configured to provide an RF ground to thesetwo photodiodes. A smaller capacitor labeled C₂ is similarlyelectrically connected between a second ground terminal 354 ₂ andphotodiode PD₂ to provide an RF ground to this photodiode. The groundterminals 354 ₁ and 354 ₂ are also electrically connected to an outputterminal 356 via resistors R₁ and R₂, respectively. Output terminal 356is electrically connected to photodiodes PD₁-PD₃ via a common electricalline 352.

Note that photodiodes PD₁ and PD₃ have the same orientation on substrate301, whereas the orientation of photodiode PD₂ is different by 180degrees. Common electrical line 352 is connected to electrical contactslocated at the right side (in the view shown in FIG. 3) of photodiodesPD₁-PD₃. Due to the orientation difference between the photodiodes, thephotocurrents generated by photodiodes PD₁ and PD₃ and the photocurrentgenerated by photodiode PD₂ are picked up by common electrical line 352and applied to output terminal 356 with opposite polarities.

A person of ordinary skill in the art will recognize that circuit 300can operate as an FIR filter whose transfer function is represented bythe following z-transform:

H(z)=1−β₁ z ⁻¹+β₂ z ²   (7)

where β₁=a₂/a₁, and β₂=a₃/a₁. Note that, in this z-transform, thezero-order and second-order tap coefficients are positive, whereas thefirst-order tap coefficient is negative. The signs of the tapcoefficients are fixed and do not change when phase shifters 306 ₁ and306 ₂ are tuned.

FIG. 4 shows a top view of an integrated optoelectronic circuit 400according to yet another embodiment of the disclosure. Circuit 400 maybe considered as an embodiment of circuit 100 (FIG. 1) corresponding toN=4. All components of circuit 400 may be fabricated on a common planarsubstrate 401 using a silicon photonic technology.

Circuit 400 has an input waveguide 402 configured to feed light into anoptical-waveguide structure comprising three optical-waveguide MZI's 404₁-404 ₃ interconnected as indicated in FIG. 4. The four outputwaveguides of this optical-waveguide structure are labeled 422 ₁-422 ₄,respectively. One arm of each MZI 404 has a respective thermoelectricphase shifter 406.

The relative intensity of light in waveguides 422 ₁-422 ₄ can be changedby appropriately tuning phase shifters 406 ₁-406 ₃ using control signals462 ₁-462 ₃, respectively. In an example embodiment, a control signal462 may be an externally generated voltage applied to a respective pairof electrical-contact pads 408 and configured to resistively heat therespective phase shifter 406. Similar to the optical-waveguide structurelocated between waveguide 302 and waveguides 322 ₁-322 ₃ in circuit 300(FIG. 3), the optical-waveguide structure located between waveguide 402and waveguides 422 ₁-422 ₄ in circuit 400 is configured to operate bothas an optical splitter analogous to optical splitter 110 (FIG. 1) and asa variable attenuator analogous to attenuator array 120 (FIG. 1).

Each of waveguides 422 ₁-422 ₄ is connected to a respective one ofwaveguides 432 ₁-432 ₄ via a respective one of fixed delay lines D₁-D₄.Each of delay lines D₁-D₄ comprises a respective length of opticalwaveguide. The waveguides in delay lines D₂, D₃, and D₄ are arranged ina double-spiral pattern. Delay line D₁ has the shortest length among thefour delay lines and, as such, imposes the shortest delay time. Delaylines D₂ and D₃ have the same nominal length. Delay line D₄ has thelongest length among the four delay lines and, as such, imposes thelongest delay time. In an example embodiment, the delay times imposed bydelay lines D₁-D₄ are τ₁, τ₁+τ₀, τ₁+τ₀, and τ₁+2T₀, respectively.

Waveguides 432 ₁-432 ₄ are configured to feed light into photodiodesPD₁-PD₄, respectively. A relatively large capacitor labeled C₁+C₃+C₄that is electrically connected between a first ground terminal 454 ₁ andphotodiodes PD₁, PD₃, and PD₄ is configured to provide an RF ground tothese three photodiodes. A smaller capacitor labeled C₂ is similarlyelectrically connected between a second ground terminal 454 ₂ andphotodiode PD₂ to provide an RF ground to this photodiode. The groundterminals 454 ₂ and 454 ₂ are also electrically connected to an outputterminal 456 via resistors R₁ and R₂, respectively. Output terminal 456is electrically connected to photodiodes PD₁-PD₄ via a common electricalline 452.

Note that photodiodes PD₁, PD₃, and PD₄ have the same orientation onsubstrate 401, whereas the orientation of photodiode PD₂ is different by180 degrees. Common electrical line 452 is connected to electricalcontacts located at the right side (in the view shown in FIG. 4) ofphotodiodes PD₁-PD₄. Due to the orientation difference between thephotodiodes, the photocurrents generated by photodiodes PD₁, PD₃, andPD₄ and the photocurrent generated by photodiode PD₂ are picked up bycommon electrical line 452 and applied to output terminal 456 withopposite polarities.

A person of ordinary skill in the art will recognize that circuit 400can operate as an FIR filter whose transfer function is represented bythe following z-transform:

H(z)=1+(β₂−β₁)z ⁻¹+β₃ z ⁻²   (8)

where β₁=a₂/a₁, β₂=a₃/a₁, and β₃=a₄/a₁. Note that, in this z-transform,the zero-order and second-order tap coefficients are positive, whereasthe first-order tap coefficient may be either positive or negative. Morespecifically, the first-order tap coefficient is positive when β₂>β₁,and negative when β₂<β₁. The sign of the first-order tap coefficient maybe changed by appropriately tuning phase shifters 406 ₁-406 ₃.

According to an example embodiment disclosed above in reference to FIGS.1-4, provided is an apparatus (e.g., 100, FIG. 1) comprising: an opticalsplitter (e.g., 110, FIG. 1) having an optical input port (e.g., for102, FIG. 1) and a plurality of optical output ports (e.g., for 112₁-112 _(N), FIG. 1); an array (e.g., 120, FIG. 1) of variableoptical-gain elements (e.g., A₁-A_(N), FIG. 1), each coupled to arespective one of the optical output ports and configured to generate arespective attenuated or amplified light beam (e.g., 122 ₁-122 _(N),FIG. 1); a bank (e.g., 130, FIG. 1) of optical delay elements (e.g.,D₁-D_(N), FIG. 1), each connected to a respective one of the variableoptical-gain elements and configured to delay the respective attenuatedor amplified light beam by a respective delay time to produce arespective delayed light beam (e.g., 132 ₁-132 _(N), FIG. 1), wherein aset of the respective delay times has at least three different values(e.g., τ₁, τ₁+τ₀, and τ₁+2τ₀); an array (e.g., 140, FIG. 1) ofphotodetectors (e.g., PD₁-PD_(N), FIG. 1), each coupled to receive lightfrom a respective one of the optical delay elements and configured toconvert the respective delayed light beam into a respective electricalsignal (e.g., 142 ₂-142 _(N), FIG. 1); and an electrical signal combiner(e.g., 150, FIG. 1) configured to combine the respective electricalsignals to generate an electrical output signal (e.g., 152, FIG. 1) in amanner that causes a first subset of the photodetectors and a secondsubset of the photodetectors to contribute the respective electricalsignals to the electrical output signal with opposite polarities.

According to another example embodiment disclosed above in reference toFIGS. 1-4, provided is an apparatus (e.g., 100, FIG. 1) comprising: anarray (e.g., 140, FIG. 1) of photodetectors (e.g., PD₁-PD_(N), FIG. 1);an optical splitter (e.g., 110, FIG. 1) having an optical input port(e.g., for 102, FIG. 1) and a plurality of optical output ports (e.g.,for 112 ₁-112 _(N), FIG. 1), with each of the optical output ports beingconnected to illuminate a respective one of the photodetectors in thearray of photodetectors; a bank (e.g., 130, FIG. 1) of optical delayelements (e.g., D₁-D_(N), FIG. 1), with each of the optical delayelements being coupled between a respective one of the optical outputports and the respective one of the photodetectors such that light ofeach of the optical output ports passes through a respective one of theoptical delay elements; and an array (e.g., 120, FIG. 1) of variableoptical-gain elements (e.g., A₁-A_(N), FIG. 1) coupled between theoptical splitter and the array of photodetectors such that, for at leastsome of the optical output ports, the light also passes through arespective one of the variable optical-gain elements. Each photodetectorin the array of photodetectors is configured to convert received lightinto a respective electrical signal. The apparatus further comprises anelectrical signal combiner (e.g., 150, FIG. 1) configured to combine therespective electrical signals to generate an electrical output signal(e.g., 152, FIG. 1) in a manner that causes a first subset of thephotodetectors and a second subset of the photodetectors to contributethe respective electrical signals to the electrical output signal withopposite polarities.

In some embodiments of the above apparatus, the array of photodetectorscomprises three photodiodes (e.g., PD₁-PD₃, FIG. 3).

In some embodiments of any of the above apparatus, the array of variableoptical-gain elements comprises one or more variable optical attenuatorsor one or more variable-gain optical amplifiers (e.g., A₁-A_(N), FIG.1).

In some embodiments of any of the above apparatus, the array ofphotodetectors comprises four photodiodes (e.g., PD₁-PD₄, FIG. 4).

In some embodiments of any of the above apparatus, the optical splitteris an optical power splitter configured to split light applied to theoptical input port into a plurality of optical beams of substantially(e.g., within 10%) equal intensities and output each of said opticalbeams through a respective one of the optical output ports.

In some embodiments of any of the above apparatus, the optical splitterand the array of variable optical-gain elements are implemented as anoptical circuit that comprises two or more Mach-Zehnder interferometers(e.g., 406, FIG. 4).

In some embodiments of any of the above apparatus, two Mach-Zehnderinterferometers (e.g., 406 ₁ and 406 ₂, FIG. 4) of the two or moreMach-Zehnder interferometers are serially connected with one another.

In some embodiments of any of the above apparatus, two Mach-Zehnderinterferometers (e.g., 406 ₃ and 406 ₂, FIG. 4) of the two or moreMach-Zehnder interferometers are connected in parallel with one another.

In some embodiments of any of the above apparatus, at least one opticaldelay element in the bank of optical delay elements is tunable (e.g.,under control of 164, FIG. 1) to change its respective delay time.

In some embodiments of any of the above apparatus, the apparatus furthercomprises an electronic controller (e.g., 160, FIG. 1) operativelycoupled to the array of variable optical-gain elements and the bank ofoptical delay elements and configured to: cause at least one of thevariable optical-gain elements to change an amount of light attenuationor amplification therein; and cause at least one optical delay elementin the bank of optical delay elements to change the respective delaytime.

In some embodiments of any of the above apparatus, the bank of opticaldelay elements includes a first optical delay element (e.g., D₂, FIG. 4)and a second optical delay element (e.g., D₃, FIG. 4) that areconfigured to delay the light by the respective delay times that arenominally identical to one another.

In some embodiments of any of the above apparatus, the array ofphotodetectors comprises a first photodetector (e.g., PD₂, FIG. 4)coupled to receive light through the first optical delay element, and asecond photodetector (e.g., PD₃, FIG. 4) coupled to receive lightthrough the second optical delay element.

In some embodiments of any of the above apparatus, the firstphotodetector belongs to the first subset of the photodetectors, and thesecond photodetector belongs to the second subset of the photodetectors.

In some embodiments of any of the above apparatus, each of the opticaldelay elements is configured to delay the light by a respective delaytime, wherein a set of the respective delay times has at least threedifferent values.

In some embodiments of any of the above apparatus, the set of therespective delay times includes the following values:

τ_(n)=τ₁+(n−1) τ₀,

where τ_(n) is the respective delay time of an n-th delay element in thebank of optical delay elements; and τ₁ and τ₀ are constants.

In some embodiments of any of the above apparatus, the optical splitter,the array of variable optical-gain elements, the bank of optical delayelements, the array of photodetectors, and the electrical signalcombiner are fabricated on a common substrate (e.g., 401, FIG. 4) toform an integrated optoelectronic circuit (e.g., 400, FIG. 4).

In some embodiments of any of the above apparatus, the apparatus isconfigured to operate as a finite-impulse-response filter that isconfigured to: variously delay two or more copies of an optical inputsignal received at the optical input port using the bank of opticaldelay elements to generate a plurality of filter-tap signals;individually weight the filter-tap signals using the array of variableoptical-gain elements to generate a plurality of weighted signals; andsum the weighted signals using the electrical signal combiner togenerate the electrical output signal.

In some embodiments of any of the above apparatus, at least one of aplurality of tap coefficients applied to weight the filter-tap signalsis positive, and at least one of the plurality of tap coefficientsapplied to weight the filter-tap signals is negative (e.g., as indicatedin Eq. (4)).

In some embodiments of any of the above apparatus, at least one of aplurality of tap coefficients applied to weight the filter-tap signalsis variable between a positive value and a negative value (e.g., asindicated in Eq. (8)).

In some embodiments of any of the above apparatus, the bank of opticaldelay elements is configured to cause the finite-impulse-response filterto have equally spaced taps (e.g., as indicated in Eq. (2) or Eq. (5)).

In some embodiments of any of the above apparatus, the apparatus furthercomprises an electronic controller (e.g., 160, FIG. 1) operativelycoupled to the array of variable optical-gain elements and configured tocause the electrical output signal to be equalized to at least partiallycompensate an effect of a transmission impairment imposed onto theoptical input signal.

In some embodiments of any of the above apparatus, the transmissionimpairment includes one or more of: (i) chromatic dispersion; (ii)polarization-mode dispersion; (iii) inter-symbol interference, and (iv)narrow-passband filtering.

According to yet another example embodiment disclosed above in referenceto FIGS. 1-4, provided is an apparatus (e.g., 100, FIG. 1) comprising:an optical splitter (e.g., 110, FIG. 1) having an optical input port(e.g., for 102, FIG. 1) and first and second optical output ports (e.g.,for 112 ₁-112 ₂, FIG. 1); a first variable optical-gain element (e.g.,A₁, FIG. 1) coupled to receive light from the first optical output portand configured to generate a first attenuated or amplified light beam(e.g., 122 ₁, FIG. 1); a second variable optical-gain element (e.g., A₂,FIG. 1) coupled to receive light from the second optical output port andconfigured to generate a second attenuated or amplified light beam(e.g., 122 ₂, FIG. 1); a first optical delay element (e.g., D₁, FIG. 1)configured to delay the first attenuated light beam by a first delaytime to produce a first delayed light beam (e.g., 132 ₁, FIG. 1); asecond optical delay element (e.g., D₂, FIG. 1) configured to delay thesecond attenuated light beam by the first delay time to produce a seconddelayed light beam (e.g., 132 ₂, FIG. 1); a first photodetector (e.g.,PD₁, FIG. 1) configured to convert the first delayed light beam into afirst electrical signal (e.g., 142 ₁, FIG. 1); a second photodetector(e.g., PD₂, FIG. 1) configured to convert the second delayed light beaminto a second electrical signal (e.g., 142 ₂, FIG. 1); and an electricalcircuit (e.g., 150, FIG. 1) configured to generate an electrical outputsignal (e.g., 152, FIG. 1) using the first and second electricalsignals, wherein the first and second electrical signals are combinedwith opposite polarities; and wherein the first and second variableoptical-gain elements are tunable such that a combined contribution ofthe first and second electrical signals into the electrical outputsignal is variable between being positive and being negative (e.g., asindicated in Eq. (8)).

While this disclosure includes references to illustrative embodiments,this specification is not intended to be construed in a limiting sense.

As used in the claims, the term “variable optical-gain element” shouldbe construed to cover both a variable optical attenuator and avariable-gain optical amplifier.

Various modifications of the described embodiments, as well as otherembodiments within the scope of the disclosure, which are apparent topersons skilled in the art to which the disclosure pertains are deemedto lie within the principle and scope of the disclosure, e.g., asexpressed in the following claims.

Unless explicitly stated otherwise, each numerical value and rangeshould be interpreted as being approximate as if the word “about” or“approximately” preceded the value or range.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this disclosure may bemade by those skilled in the art without departing from the scope of thedisclosure, e.g., as expressed in the following claims.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of thedisclosure. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment, nor are separate or alternative embodiments necessarilymutually exclusive of other embodiments. The same applies to the term“implementation.”

Also for purposes of this description, the terms “couple,” “coupling,”“coupled,” “connect,” “connecting,” or “connected” refer to any mannerknown in the art or later developed in which energy is allowed to betransferred between two or more elements, and the interposition of oneor more additional elements is contemplated, although not required.Conversely, the terms “directly coupled,” “directly connected,” etc.,imply the absence of such additional elements.

The described embodiments are to be considered in all respects as onlyillustrative and not restrictive. In particular, the scope of thedisclosure is indicated by the appended claims rather than by thedescription and figures herein. All changes that come within the meaningand range of equivalency of the claims are to be embraced within theirscope.

A person of ordinary skill in the art would readily recognize that stepsof various above-described methods can be performed by programmedcomputers. Herein, some embodiments are intended to cover programstorage devices, e.g., digital data storage media, which are machine orcomputer readable and encode machine-executable or computer-executableprograms of instructions where said instructions perform some or all ofthe steps of methods described herein. The program storage devices maybe, e.g., digital memories, magnetic storage media such as a magneticdisks or tapes, hard drives, or optically readable digital data storagemedia. The embodiments are also intended to cover computers programmedto perform said steps of methods described herein.

The description and drawings merely illustrate the principles of thedisclosure. It will thus be appreciated that those of ordinary skill inthe art will be able to devise various arrangements that, although notexplicitly described or shown herein, embody the principles of thedisclosure and are included within its spirit and scope. Furthermore,all examples recited herein are principally intended expressly to beonly for pedagogical purposes to aid the reader in understanding theprinciples of the disclosure and the concepts contributed by theinventor(s) to furthering the art, and are to be construed as beingwithout limitation to such specifically recited examples and conditions.Moreover, all statements herein reciting principles, aspects, andembodiments of the disclosure, as well as specific examples thereof, areintended to encompass equivalents thereof.

The functions of the various elements shown in the figures, includingany functional blocks labeled as “controllers” and “processors,” may beprovided through the use of dedicated hardware as well as hardwarecapable of executing software in association with appropriate software.When provided by a processor, the functions may be provided by a singlededicated processor, by a single shared processor, or by a plurality ofindividual processors, some of which may be shared. Moreover, explicituse of the term “processor” or “controller” should not be construed torefer exclusively to hardware capable of executing software, and mayimplicitly include, without limitation, digital signal processor (DSP)hardware, network processor, application specific integrated circuit(ASIC), field programmable gate array (FPGA), read only memory (ROM) forstoring software, random access memory (RAM), and non volatile storage.Other hardware, conventional and/or custom, may also be included.Similarly, any switches shown in the figures are conceptual only. Theirfunction may be carried out through the operation of program logic,through dedicated logic, through the interaction of program control anddedicated logic, or even manually, the particular technique beingselectable by the implementer as more specifically understood from thecontext.

1. An apparatus comprising: an array of photodetectors; an opticalsplitter having an optical input port and a plurality of optical outputports, with each of the optical output ports being connected toilluminate a respective one of the photodetectors in the array ofphotodetectors; a bank of optical delay elements, with each of theoptical delay elements being coupled between a respective one of theoptical output ports and the respective one of the photodetectors suchthat light of each of the optical output ports passes through arespective one of the optical delay elements; and an array of variableoptical-gain elements coupled between the optical splitter and the arrayof photodetectors such that, for at least some of the optical outputports, the light also passes through a respective one of the variableoptical-gain elements; wherein each photodetector in the array ofphotodetectors is configured to convert received light into a respectiveelectrical signal; wherein the apparatus further comprises an electricalsignal combiner configured to combine the respective electrical signalsto generate an electrical output signal in a manner that causes a firstsubset of the photodetectors and a second subset of the photodetectorsto contribute the respective electrical signals to the electrical outputsignal with opposite polarities; and wherein the apparatus furthercomprises an electronic controller operatively coupled to the bank ofoptical delay elements and configured to cause at least one opticaldelay element in the bank of optical delay elements to change arespective delay time.
 2. The apparatus of claim 1, wherein the array ofvariable optical-gain elements comprises one or more variable opticalattenuators or one or more variable-gain optical amplifiers.
 3. Theapparatus of claim 1, wherein the array of photodetectors comprisesthree photodiodes.
 4. The apparatus of claim 1, wherein the opticalsplitter is an optical power splitter configured to split light appliedto the optical input port into a plurality of optical beams ofsubstantially equal intensities and output each of said optical beamsthrough a respective one of the optical output ports.
 5. The apparatusof claim 1, wherein the optical splitter and the array of variableoptical-gain elements are implemented as an optical circuit thatcomprises two or more Mach-Zehnder interferometers.
 6. The apparatus ofclaim 5, wherein two Mach-Zehnder interferometers of the two or moreMach-Zehnder interferometers are serially connected with one another. 7.The apparatus of claim 5, wherein two Mach-Zehnder interferometers ofthe two or more Mach-Zehnder interferometers are connected in parallelwith one another.
 8. (canceled)
 9. The apparatus of claim 1, wherein theelectronic controller is further operatively coupled to the array ofvariable optical-gain elements and further configured to cause at leastone of the variable optical-gain elements to change an amount of lightamplification therein.
 10. The apparatus of claim 1, wherein the bank ofoptical delay elements includes a first optical delay element and asecond optical delay element that are configured to delay the light byrespective delay times that are nominally identical to one another. 11.The apparatus of claim 10, wherein the array of photodetectors comprisesa first photodetector coupled to receive light through the first opticaldelay element and a second photodetector coupled to receive lightthrough the second optical delay element; and wherein the firstphotodetector belongs to the first subset of the photodetectors, and thesecond photodetector belongs to the second subset of the photodetectors.12. The apparatus of claim 1, wherein each of the optical delay elementsis configured to delay the light by a respective delay time, wherein aset of the respective delay times has at least three different values.13. The apparatus of claim 12, wherein the set of the respective delaytimes includes the following values:τ_(n)=τ₁+(n−1) τ₀, where τ_(n) is the respective delay time of an n-thdelay element in the bank of optical delay elements; and τ₁ and τ₀ areconstants.
 14. The apparatus of claim 1, wherein the apparatus isconfigured to operate as a finite-impulse-response filter that isconfigured to: variously delay two or more copies of an optical inputsignal received at the optical input port using the bank of opticaldelay elements to generate a plurality of filter-tap signals;individually weight the filter-tap signals using the array of variableoptical-gain elements to generate a plurality of weighted signals; andsum the weighted signals using the electrical signal combiner togenerate the electrical output signal.
 15. The apparatus of claim 14,wherein at least one of a plurality of tap coefficients applied toweight the filter-tap signals is positive, and at least one of theplurality of tap coefficients applied to weight the filter-tap signalsis negative.
 16. The apparatus of claim 14, wherein at least one of aplurality of tap coefficients applied to weight the filter-tap signalsis variable between a positive value and a negative value.
 17. Theapparatus of claim 14, wherein the bank of optical delay elements isconfigured to cause the finite-impulse-response filter to have equallyspaced taps. 18-20. (canceled)
 21. An apparatus comprising: an array ofphotodetectors; an optical splitter having an optical input port and aplurality of optical output ports, with each of the optical output portsbeing connected to illuminate a respective one of the photodetectors inthe array of photodetectors; a bank of optical delay elements, with eachof the optical delay elements being coupled between a respective one ofthe optical output ports and the respective one of the photodetectorssuch that light of each of the optical output ports passes through arespective one of the optical delay elements; and an array of variableoptical-gain elements coupled between the optical splitter and the arrayof photodetectors such that, for at least some of the optical outputports, the light also passes through a respective one of the variableoptical-gain elements; wherein each photodetector in the array ofphotodetectors is configured to convert received light into a respectiveelectrical signal; wherein the apparatus further comprises an electricalsignal combiner configured to combine the respective electrical signalsto generate an electrical output signal in a manner that causes a firstsubset of the photodetectors and a second subset of the photodetectorsto contribute the respective electrical signals to the electrical outputsignal with opposite polarities; and wherein the optical splitter andthe array of variable optical-gain elements are implemented as anoptical circuit that comprises two or more Mach-Zehnder interferometers.22. The apparatus of claim 21, wherein two Mach-Zehnder interferometersof the two or more Mach-Zehnder interferometers are serially connectedwith one another.
 23. The apparatus of claim 21, wherein twoMach-Zehnder interferometers of the two or more Mach-Zehnderinterferometers are connected in parallel with one another.
 24. Anapparatus comprising: an array of photodetectors; an optical splitterhaving an optical input port and a plurality of optical output ports,with each of the optical output ports being connected to illuminate arespective one of the photodetectors in the array of photodetectors; abank of optical delay elements, with each of the optical delay elementsbeing coupled between a respective one of the optical output ports andthe respective one of the photodetectors such that light of each of theoptical output ports passes through a respective one of the opticaldelay elements; and an array of variable optical-gain elements coupledbetween the optical splitter and the array of photodetectors such that,for at least some of the optical output ports, the light also passesthrough a respective one of the variable optical-gain elements; whereineach photodetector in the array of photodetectors is configured toconvert received light into a respective electrical signal; wherein theapparatus further comprises an electrical signal combiner configured tocombine the respective electrical signals to generate an electricaloutput signal in a manner that causes a first subset of thephotodetectors and a second subset of the photodetectors to contributethe respective electrical signals to the electrical output signal withopposite polarities; wherein each of the optical delay elements isconfigured to delay the light by a respective delay time, wherein a setof the respective delay times has at least three different values; andwherein the set of the respective delay times includes the followingvalues:τ_(n)=τ₁+(n−1) τ₀, where τ_(n) is the respective delay time of an n-thdelay element in the bank of optical delay elements; and τ₁ and τ₀ areconstants.